What is the integral of (x+8)/(2x^3-8x) ?

The integral of (x+8)/(2x^3-8x) is -ln|x|+3/8 ln|x+2|+5/8 ln|x-2|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (x+8)/(2x^3-8x)

\int \frac{x + 8}{2 x ^{3} - 8 x} d x

- ln ∣ x ∣ + \frac{3}{8} ln ∣ x + 2 ∣ + \frac{5}{8} ln ∣ x - 2 ∣ + C

Solution steps

\int \frac{x + 8}{2 x ^{3} - 8 x} d x

Take the partial fraction of

\frac{x + 8}{2 x ^{3} - 8 x} : - \frac{1}{x} + \frac{3}{8 ( x + 2 )} + \frac{5}{8 ( x - 2 )}

= \int - \frac{1}{x} + \frac{3}{8 ( x + 2 )} + \frac{5}{8 ( x - 2 )} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - \int \frac{1}{x} d x + \int \frac{3}{8 ( x + 2 )} d x + \int \frac{5}{8 ( x - 2 )} d x

\int \frac{1}{x} d x = ln ∣ x ∣

\int \frac{3}{8 ( x + 2 )} d x = \frac{3}{8} ln ∣ x + 2 ∣

\int \frac{5}{8 ( x - 2 )} d x = \frac{5}{8} ln ∣ x - 2 ∣

= - ln ∣ x ∣ + \frac{3}{8} ln ∣ x + 2 ∣ + \frac{5}{8} ln ∣ x - 2 ∣

Add a constant to the solution

= - ln ∣ x ∣ + \frac{3}{8} ln ∣ x + 2 ∣ + \frac{5}{8} ln ∣ x - 2 ∣ + C

\int \frac{4}{1 + y ^{2}} d y

\int 1 + \frac{4}{9} x^{- \frac{2}{3}} d x

\int x (1 + x)^{3} d x

\int t^{5} sin (t^{6}) d t

\int \frac{x ^{7} + x ^{2} + 1}{x ^{2}} d x

What is the integral of (x+8)/(2x^3-8x) ?
The integral of (x+8)/(2x^3-8x) is -ln|x|+3/8 ln|x+2|+5/8 ln|x-2|+C